Chapter 4

Triangles, Quadrilaterals and Constructions!

This is exam revision for chapter 4 in the 'Essential Mathhematics VELS Edition for Year 7'. Chapter 4 is all about triangles, quadrilaterals and constructions. I hope that this page is useful for your upcoming exam, as a lot of hard work and effort has gone into creating it! Let's get studying!

4.1 - Naming and measuring angles

What is an angle?
An angle is formed when two lines (called arms) meet at a point known as the vertix.

Angle sizes

Angle type	Angle Size	Example
Acute Angle	Between 0 and 90 degrees
Right Angle	Exactly 90 degreesYou will know if something has/is a rightangle, as there will be a box, instead of a circular shape
Straight Angle	Exactly 180 degrees
Obtuse Angle	Any size between 90 and 180 degrees
Reflex Angle	Any size between 180 and 360 degrees
Circular Angle/ perigon/ Revolution	One complete turn

QUIZ TIME!

How big are these angles?
1.

2.

3.


Anwsers:
1 - 120 Degrees
2 - 100 Degrees
3 - 30 Degrees

4.2 - Scalene, Equilateral and Isosceles Triangles

What is a triangle?

A triangle is a three sided shape, which every line meets another at a vertix. Differently shaped triangles have different names. Angles are classified by the property of their sides.

Different Triangles -

Name	Shape	Number of equal sides	Number of equal angles
Equilateral Triangle		3	3 - Each angle must be the same, and every side must be the same
Isosceles Triangle		2	2 - Two angles must be the same, as do two sides, the third angle/side must be different to the others
Scalene Triangle		0	0 - Every angle/side must be different. If any sides are the same it isn't Scalene

QUIZ TIME!

Classify each of the following angles
1.

2.

3.

Answers:
1 - Scalene
2 - Equilateral
3 - Isoceles

4.3 - Right-Angled, Acute Angled and Obtuse Angled Triangles

Triangles can be classified by the size of their angles.

If every angle in the triangle is acute, then it can be classified an acute-angled triangle -


If the triangle has one right angle, then it can be classified a right-angled triangle -


If the triangle has one obtuse angle, then it can be classified as an obutse-angled triangle -

QUIZ TIME!

Please classify the following triangles:

1.

2.


3.

Answers -
1: Acute-angled Angle
2: Obtuse-angled triangle
3: Right-angled triangle

4.4 - Drawing triangles given a combination of sides and angles

To draw any triangle, you don't have to know the lengths of all the sides and sizes of angles. But you do need some information, which is called 'sufficient information'. There are three different ways that information can be given to you and you can determind the shape/size of the triangle:

1 - The lengths of two sides and the angle between them
2 - The leghts of all three sides and no angles
3 - The length of one side and the angles at each end

4.5 - Quadrilaterals and parallelograms

What are quadrilaterals and parallelograms?
Every four sided shapes are called quadrilaterals. Similar to triangles, quadrilaterals are classified according to their shape and size.

Quadrilaterals/Parallelograms

Name	Shape	Special Properties
Parallelogram		A parallelogram is quadrilateral,with both pairs of opposite sides that are parallel. This shape has two pairs of equal sides and angles.
Rhombus/diamond		A rhombus/diamond is a parallelogram with 4 equal sides, 2 pairs of equal angles and 2 pairs of parallel sides.
Rectangle		A rectangle is a parallelogram with each angle 90 degrees.
Square		A square is a parallelogram with 4 equal sides and4 equal angles all 90 degrees.
Trapezium		A trapezium is a quadrilateral with one pair of opposite sides parallel.
Kite		A kite is a quadrilateral with two pairs of equal adjacent sides (adjacent means beside each other)or one pair of opposite angles equal.

QUIZ TIME!

Name each of the following quadrilaterals/paralellogram:
1


2

3

Answers:
1 - rectangle
2 - Rhombus/diamond
3 - Square

That's all! I hope that you found this helpful, and I KNOW that you will do very well on your end of year exam!

Bec